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Greece Junior Math Olympiad
2001 Greece Junior Math Olympiad
1
Inequality
Inequality
Source: Archimedes 2001 Junior
March 17, 2020
inequalities
Problem Statement
Let
a
,
b
,
x
,
y
a, b, x, y
a
,
b
,
x
,
y
be positive real numbers such that
a
+
b
=
1
a+b=1
a
+
b
=
1
. Prove that
1
a
x
+
b
y
≤
a
x
+
b
y
\frac{1}{\frac{a}{x}+\frac{b}{y}}\leq ax+by
x
a
+
y
b
1
≤
a
x
+
b
y
and find when equality holds.
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